Edit There appears to be a better LZW solution that handles Unicode strings correctly at http://pieroxy.net/blog/pages/lz-string/index.html (Thanks to pieroxy in the comments).
I don’t know of any gzip implementations, but the jsolait library (the site seems to have gone away) has functions for LZW compression/decompression. The code is covered under the LGPL.
// LZW-compress a string function lzw_encode(s) { var dict = {}; var data = (s + "").split(""); var out = []; var currChar; var phrase = data[0]; var code = 256; for (var i=1; i<data.length; i++) { currChar=data[i]; if (dict[phrase + currChar] != null) { phrase += currChar; } else { out.push(phrase.length > 1 ? dict[phrase] : phrase.charCodeAt(0)); dict[phrase + currChar] = code; code++; phrase=currChar; } } out.push(phrase.length > 1 ? dict[phrase] : phrase.charCodeAt(0)); for (var i=0; i<out.length; i++) { out[i] = String.fromCharCode(out[i]); } return out.join(""); } // Decompress an LZW-encoded string function lzw_decode(s) { var dict = {}; var data = (s + "").split(""); var currChar = data[0]; var oldPhrase = currChar; var out = [currChar]; var code = 256; var phrase; for (var i=1; i<data.length; i++) { var currCode = data[i].charCodeAt(0); if (currCode < 256) { phrase = data[i]; } else { phrase = dict[currCode] ? dict[currCode] : (oldPhrase + currChar); } out.push(phrase); currChar = phrase.charAt(0); dict[code] = oldPhrase + currChar; code++; oldPhrase = phrase; } return out.join(""); }